Special theory of relativity

In essence, special theory of relativity removes “relativity” from “speed of light” and attaches “relativity” to “space (distance)” and “time”. This is the difficult part. Classically, we have considered both these elements as universally invariants with respect to all frames of reference which are moving with constant relative velocity (inertial frames of reference). We shall try to come to terms with these new ideas in subsequent modules. But the essence of special theory of relativity is captured as follows : The speed of light in vacuum is invariant whereas distance between two points and time intervals are variant in the system of inertial frames of reference.

The ideas of classical relativity, where in space and time are invarinat and speed of light is variant, is captured by Galilean transformation which enables us to measure motion in two inertial frames of reference. The speed of an object is modified by the relative speed of the frames of reference.

u' = u ± v

where “u” and “u'” are the speeds of an object as measured in two frames of reference which themselves move with a speed “v” with respect to each other.

Einstein employed a different transform called “Lorentz transformation” to capture the idea of invariant speed of light and variant distance and time measurements. The Lorentz tansformation provides the exact relation between coordinates (space and time) of inertial references. We shall discuss these transformations separately in the module.

Further, since we are considering constancy of speed of light in relation to inertial references only, the special theory of relativity is “restricted” to inertial frames of reference and therefore is “special” not “general”.

Postulates of special theory of relativity

There are many versions of postulates. The essence of special theory of relativity is finally agreed to be captured by following two principles/ postulates :

1. The principle of relativity : The laws of physics are the same for all observers in uniform motion relative to one another (inertial frames of reference).

2. The principle of constancy of speed of light in vacuum : Light in vacuum propagates with the constant speed through all systems of inertial coordinates, regardless of the state of motion of the light source.

Few scholars consider either of above postulates sufficient to describe special theory of relativity. They are supplementary to each other. As a matter of fact, one can be deduced from other and vice –versa with certain extrapolation.

Proceeding from the principle of relativity, we can arrive at the principle of constancy of speed of light in vacuum. The principle of relativity considers validity of all physical laws across all inertial frames of reference. This means that law of propagation of light (electromagnetic theory) is same across coordinates systems in uniform translatory motion. But, the law of propagation of light says that light moves at a constant speed in vacuum and is independent of the motion of source. Thus, speed of light is constant in terms of any system of inertial coordinates, regardless of the state of motion of the light source. This is exactly the the principle of constancy of speed of light in vacuum.